Related papers: Dimension-free uniform concentration bound for log…
This paper extends standard results from learning theory with independent data to sequences of dependent data. Contrary to most of the literature, we do not rely on mixing arguments or sequential measures of complexity and derive uniform…
This paper is focused on dimension-free PAC-Bayesian bounds, under weak polynomial moment assumptions, allowing for heavy tailed sample distributions. It covers the estimation of the mean of a vector or a matrix, with applications to least…
Recently, there has been remarkable progress in reinforcement learning (RL) with general function approximation. However, all these works only provide regret or sample complexity guarantees. It is still an open question if one can achieve…
We investigate 1) the rate at which refined properties of the empirical risk---in particular, gradients---converge to their population counterparts in standard non-convex learning tasks, and 2) the consequences of this convergence for…
We consider the problem of predicting as well as the best linear combination of d given functions in least squares regression, and variants of this problem including constraints on the parameters of the linear combination. When the input…
We present a framework for the theoretical analysis of ensembles of low-complexity empirical risk minimisers trained on independent random compressions of high-dimensional data. First we introduce a general distribution-dependent…
We present a new PAC-Bayesian generalization bound. Standard bounds contain a $\sqrt{L_n \cdot \KL/n}$ complexity term which dominates unless $L_n$, the empirical error of the learning algorithm's randomized predictions, vanishes. We manage…
In this paper, we present a new estimator of the mean of a random vector, computed by applying some threshold function to the norm. Non asymptotic dimension-free almost sub-Gaussian bounds are proved under weak moment assumptions, using…
The method to derive uniform bounds with Gaussian and Rademacher complexities is extended to the case where the sample average is replaced by a nonlinear statistic. Tight bounds are obtained for U-statistics, smoothened L-statistics and…
We consider a problem of high-dimensional linear regression with random design. We suggest a novel approach referred to as error-in-operator which does not estimate the design covariance $\Sigma$ directly but incorporates it into empirical…
We consider the problem of predicting as well as the best linear combination of d given functions in least squares regression under L^\infty constraints on the linear combination. When the input distribution is known, there already exists…
We present a novel notion of complexity that interpolates between and generalizes some classic existing complexity notions in learning theory: for estimators like empirical risk minimization (ERM) with arbitrary bounded losses, it is upper…
In a groundbreaking work, Schmidt-Hieber (2020) proved the minimax optimality of deep neural networks with ReLu activation for least-square regression estimation over a large class of functions defined by composition. In this paper, we…
In this paper, we improve the PAC-Bayesian error bound for linear regression derived in Germain et al. [10]. The improvements are twofold. First, the proposed error bound is tighter, and converges to the generalization loss with a…
Algorithm- and data-dependent generalization bounds are required to explain the generalization behavior of modern machine learning algorithms. In this context, there exists information theoretic generalization bounds that involve (various…
We examine the concentration of uniform generalization errors around their expectation in binary linear classification problems via an isoperimetric argument. In particular, we establish Poincar\'{e} and log-Sobolev inequalities for the…
The regression function is one of the key objects of binary classification, since it not only determines a Bayes optimal classifier, hence, defines an optimal decision boundary, but also encodes the conditional distribution of the output…
The multi-index model with sparse dimension reduction matrix is a popular approach to circumvent the curse of dimensionality in a high-dimensional regression setting. Building on the single-index analysis by Alquier, P. & Biau, G. (Journal…
We present some extensions of Bernstein's concentration inequality for random matrices. This inequality has become a useful and powerful tool for many problems in statistics, signal processing and theoretical computer science. The main…
We propose data-dependent uniform generalization bounds by approaching the problem from a PAC-Bayesian perspective. We first apply the PAC-Bayesian framework on "random sets" in a rigorous way, where the training algorithm is assumed to…